7. Use Fermat's Little Theorem to find the remainders of each of the division problems a....
Discrete structures please help!! Use Fermat's little theorem to find the remainder when 91000 is divided by 13. To get credit, use Fermat's little theorem and show how each step is done without using a calculator.
(III) State Fermat's Little Theorem and use it to deduce that dp-1.
Solve the following problems using Fermat's Little Theorem (a) Prove that, if 5 does not divide n, then 5n1. (b) Prove that, if gcd(n, 6) 1, then 12n2 - 1 (c) Prove that, if 5 does not divide n-1, , or n+1, then 5(n21).
Determine the tens digit of 3^3^100 . (Hint: Use Euler's generalization of Fermat's little theorem)
solve number #7 please. domain is a field. 7. State Fermat's theorem and use it to find the remainder when 31233 is divided by 11.
7. EXTRA CREDIT [5 points] For Zp, where p is a prime, Fermat's theorem gives us an alternative way to compute the multiplicative inverse of any given nonzero [x]p: raise it to the power of p-1. Show that Fermat's theorem is a corollary (a special case) of Euler's theorem, i.e., show how one can derive the former from the latter.
D Question 5 7 pts Use division and the Remainder Theorem to find the value of P (i). Where P(x) = 624 – 2x2 + 4.
the second part of the question can be solved by the chineses remainder theorem. Problem 4 (4pts) Recalled Fermat's little theorem: For every p, a € N, if p is a prime and pla, then -I = 1 mod p. Use Fermat's little theorem to find a = 71002 mod 13) and b =(71002 mod 41). Find an 3 (0 < < 13 x 41) such that r = a (mod 13) and 2 = b (mod 41).
Use synthetic division and the Remainder Theorem to find the indicated function value. -32 7 -11 -21 By the Remainder Theorem, f(-5) = O-41 O 2x2 + 17x + 74 R 349 O 349 O 2x2 - 3x + 4 R-41 O None of these
r proof of Fermat's little theo- 2. Use Corollary 3.6 to give anothe Proposition 3.3 of Chapter 1. (Hint: In our more up-to-date language, the theorem should be restated as follows: given any prime number p, a. a for all a E Zp.) rem, Corollary 3.6. If IGI n, and a E G is arbitrary, then ane. Proof. Let the order of the element a be k. By Corollary 3.4, k n, so there is an integer e with n...